Option Investor Rationality Revisited: The Role of Exercise Boundary Violations

Abstract

The authors dispute the theory that American call options should not be exercised early. By looking at intraday pricing, they find that the best bid price available is often lower than the option’s intrinsic value and early exercise can be rational.

Our empirical results overturn the well-known textbook theory that American options should not be exercised early except in very limited conditions. In the real world, the best bid available in the market is frequently below the option’s intrinsic value (e.g., nearly half of all quotes for in-the- money calls), which we call an “exercise boundary violation” (EBV). In an EBV, early exercise can be the right strategy and the “American” option characteristic has economic value. Some option holders do exercise, some sell at EBV bid prices, and our results suggest that actual exercise behavior is much less irrational than earlier studies concluded.

Disclosure: The authors report no conflicts of interest.

Editor’s Notes

Submitted 26 May 2019

Accepted 4 November 2019 by Stephen J. Brown.

This article was externally reviewed using our double-blind peer-review process. When the article was accepted for publication, the authors thanked the reviewers in their acknowledgments. Giuseppe Ballocchi, CFA, and William Fung were the reviewers for this article.

Acknowledgment

We are grateful for the comments from Jason Bristol, Giuseppe Ballocchi, CFA, Stephen Brown, Josh Coval, William Fung, Bob Jennings, Craig Holden, Samuel Kadzieala, Andrew Kung, CFA, Chien-Ling Lo, Veronika Krepely Poole, Sheldon Natenberg, Jason Smith, Lars Stentoft, Chuck Trzcinka, Tim Weithers, Adam Westergaard, and the seminar participants at Indiana University, IFSID 2014, New Frontiers in Finance: Options and Volatility Conference at Vanderbilt University, European Financial Management Association meetings in 2016 and 2017, 2016 China International Conference in Finance, New York University, McGill University, Florida International University, and Auburn University. Stephen Figlewski thanks the Nasdaq Educational Foundation for financial support. Robert Whaley generously provided the exercise data for this article.

Notes

¹ A model for the liquidity value of the option to exit an American call position early without giving up an EBV was developed by Figlewski (2019). For a sample of large stocks with active option trading, the value of American exercise to avoid an EBV was found to be frequently of comparable size to or larger than the value to get a dividend. This liquidity value is on top of any dividend-related premium from the American exercise.

² By placing a limit sell order inside the spread, at S – X (stock price minus strike price), for example, the investor would be supplying liquidity to the market and would avoid giving up the half-spread if the order were executed. But placing the order should not cause option market makers to raise their bid prices, so execution would require the arrival of a matching buy order from an outside investor. Unless that order arrived immediately, the stock price would move and the market makers would update their quotes. On the one hand, if the call price drifted downward, their ask price would eventually be below the investor’s limit price and the order would not execute at all. If call prices rose, on the other hand, the market-maker bid would eventually equal the limit price and the order would execute. That price would again, however, be below the updated intrinsic value. In order to actually liquidate the call option at intrinsic value, the investor would not only have to place the limit order at S – X but also continuously adjust it to remain inside the market makers’ quotes as the stock price fluctuated. In other words, the investor would need to monitor the market as closely as a market maker does until the necessary outside order arrived. For many in-the-money options, this could take days. Trying to capture the option’s intrinsic value by placing a limit order inside the posted quotes is viable only in a very liquid option market with frequent order flow from non-market makers.

³ Although our sample contains more than a billion option quotes, it covers only 21 trading days, which raises a potential concern that the EBVs we report might have been a temporary market aberration in this period. We found similar results, however, in intraday data for August 2008. Simple observation of trading in the option market reveals EBVs for ITM options that are not far from expiration common in posted option quotes every day. Also, Figlewski (2019) looked at end-of-day option quotes on major stocks in a later sample period, 2016–2017, and found the same pervasive underbids. EBVs are a broad and persistent phenomenon. The prevalence of EBVs is related to option moneyness, which varies over time. In periods of low implied volatility and low interest rates, which have characterized the market for much of the period since 2010, EBVs become even more prevalent. The example of ExxonMobil options described previously came during such a period.

⁴ The Option Clearing Corporation data were generously provided to us by Robert Whaley of Vanderbilt University.

⁵ Saraoglu, Louton, and Holowczak (2014) examined the impact of the Penny Pilot Program on option-trading costs.

⁶ Similar results were found when we sampled observations at 11:00 a.m., 12:00 noon, and 2:00 p.m.

⁷ In theory, delta hedging allows recovery of an option’s full value, not only its intrinsic value, which makes it better than exercise in a frictionless world. The intrinsic value is embedded in the difference between the current stock price and the strike, but replicating the optionality value requires (frictionless) continuous rebalancing of the hedge. Frequent rebalancing in the real world quickly leads to large transaction costs, and it still does not fully eliminate risk.

⁸ Measuring execution quality by the difference between the trade price and the quote midpoint and then examining whether execution quality improved when the boundary violations were large might seem reasonable because investors have more possibilities to trade inside the spread. Unfortunately, this idea does not work because investors trying to escape EBVs can be expected to try placing limit orders inside the market makers’ spread, which alters the recorded best prices. We argue later that a more appropriate approach in an EBV would be to treat the option’s intrinsic value as the market’s best bid.

⁹ Examples include Diz and Finucane (1993), Overdahl and Martin (1994), Finucane (1997), Engström (2002), Pool et al. (2008), Hao et al. (2010), Barraclough and Whaley (2012), and Jensen and Pedersen (2016).

¹⁰ Barraclough and Whaley (2012) also found that market makers exhibit early exercise behavior that runs counter to conventional theory.

¹¹ Exchanges introduce option strikes around the current underlying stock price, and as the stock price moves, new strikes are introduced while existing options may go deep in or out of the money. A moderate advance in the stock market in the months before March 2010 left many of the previously introduced calls deep in the money and the corresponding puts out of the money (and out of our sample).